Article
Mathematics, Applied
Jishan Fan, Xin Zhong
Summary: By applying delicate energy estimates, we demonstrate regularity criteria for strong solutions to the 3D nonhomogeneous magneto-micropolar fluid equations with vacuum.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
Fan Wu
Summary: The study presents a sufficient condition to ensure the smoothness of solutions to 3D magneto-micropolar fluid equations by refining and extending previous results in incompressible Navier-Stokes equations, micropolar fluid equations, and MHD equations.
JOURNAL OF EVOLUTION EQUATIONS
(2021)
Article
Mathematics, Applied
Ines Ben Omrane, Mourad Ben Slimane, Sadek Gala, Maria Alessandra Ragusa
Summary: This paper investigates the regularity criteria for the 3D micropolar fluid equations in terms of pressure in weak Lebesgue space. It is proven that the weak solution is regular on (0, T] if the pressure satisfies either the norm IIπIILα,∞(0,T;Lβ,∞(R3)) with 2α+β/3=2 and 32<β<∞ or IIVπIILα,∞(0,T;Lβ,∞(R3)) with 2α+β/3=3 and 1<β<∞ is sufficiently small.
Article
Mathematics, Applied
Zhouyu Li, Pengcheng Niu
Summary: This paper examines the regularity of weak solutions to the 3D magneto-micropolar fluid equations, showing that if the velocity field or pressure belongs to certain Lorentz spaces in both time and spatial directions, the weak solutions are regular on [0, T]. Additionally, regularity criteria are obtained for the micropolar fluid equations and the MHD equations, respectively, extending and generalizing previous results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics
Ravi P. Agarwal, Ahmad M. Alghamdi, Sadek Gala, Maria Alessandra Ragusa
Summary: In this paper, we establish a regularity criterion for micropolar fluid flows by introducing the one component of the velocity in critical Morrey-Campanato space. Specifically, we prove that if Z0 T 24 9 symbolscript < infinity, where 0 < r < M2, 3 10, r, then the weak solution (u, w) is regular.
MATHEMATICAL MODELLING AND ANALYSIS
(2023)
Article
Mathematics
Jens Lorenz, Wilberclay G. Melo, Suelen C. P. de Souza
Summary: In this paper, we demonstrate that a weak solution of the magneto-micropolar equations, under certain conditions, is regular and can be extended as a higher order solution.
ELECTRONIC RESEARCH ARCHIVE
(2021)
Article
Physics, Mathematical
Wanping Wu, Yinghui Zhang
Summary: This paper investigates the long time behavior of solutions to the incompressible magneto-micropolar fluids in two and three dimensions. When the magnetic diffusion is absent, the L-2 norms of the fluid velocity and micro-rotational velocity tend to zero, while the L-2 norm of the magnetic field converges to a non-negative constant as time tends to infinity. Moreover, in the presence of both magnetic diffusion and spin viscosity, and with initial data belonging to L-2, the solutions decay to zero without a rate, and this non-uniform decay is optimal. The proofs rely on Fourier splitting method, low-frequency and high-frequency decomposition techniques, and careful energy estimates.
JOURNAL OF MATHEMATICAL PHYSICS
(2023)
Article
Mathematics, Applied
Yanjiao Li, Xiaojun Li
Summary: This article investigates the regularity of the statistical solution for a 2D non-autonomous magneto-micropolar fluid system, as well as the relationship between invariant measure and statistical solution. The existence and regularity of pullback attractor for the system is proved to determine the regularity of the statistical solution, which is shown to be an invariant measure for the system under consideration.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics
Hongxia Lin, Sen Liu, Heng Zhang, Ru Bai
Summary: This paper investigates the global regularity of 2D incompressible anisotropic magneto-micropolar fluid equations with partial viscosity. Compared to Ma [22], this paper studies 12 cases in [22] and some other new cases, and provides new regular conditions, improving the results in [22] in terms of weaker regular criteria.
ACTA MATHEMATICA SCIENTIA
(2023)
Article
Physics, Mathematical
Lingxi Liu, Xin Zhong
Summary: This study focuses on the initial boundary value problem of two-dimensional nonhomogeneous micropolar fluid equations with density-dependent viscosity and non-negative density. By applying the Desjardins interpolation inequality and careful energy estimates, the global existence of a unique strong solution is proven under suitable conditions. Additionally, it is shown that the velocity and micro-rotational velocity exponentially converge to zero as time approaches infinity.
JOURNAL OF MATHEMATICAL PHYSICS
(2021)
Article
Mathematics, Applied
F. W. Cruz, M. M. Novais
Summary: This paper is dedicated to studying micropolar fluids moving in the presence of a magnetic field in 3-dimensional space. We prove the global existence and uniqueness of strong solutions with small initial data.
APPLICABLE ANALYSIS
(2022)
Article
Mathematics, Applied
Huanyuan Li
Summary: This paper focuses on the Cauchy problem of the three-dimensional nonhomogeneous incompressible micropolar fluid equations in the whole space. A weak Serrin-type blowup criterion for the strong solutions is established. It is proven that the strong solution exists globally for the Cauchy problem of the three-dimensional nonhomogeneous micropolar equations if the velocity satisfies the weak Serrin's condition, irrespective of the micro-rotational velocity. As an immediate application, it is further shown that the Cauchy problem of micropolar fluid equations has a unique global strong solution when the kinematic viscosity is sufficiently large, or the upper bound of initial density or initial kinetic energy is small enough.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Chao Li, Jiayu Li, Xi Zhang
Summary: This paper discusses the Dirichlet problem of a complex Monge-Ampere equation on a ball in C-n, proving interior estimates for the solution under different types of data conditions. These estimates are generalized versions of the Bedford-Taylor interior estimate.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Yan Jia, Qianqian Xie, Bo-Qing Dong
Summary: This paper investigates the global regularity of 3D magneto-micropolar equations. Based on new observation of the nonlinear structure and sharp a priori estimates, the global existence of smooth solutions for the system with minimal dissipation is examined.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics, Applied
Caidi Zhao, Yongkang Zhang, Tomas Caraballo, Grzegorz Lukaszewicz
Summary: This paper investigates the nonautonomous micropolar fluid with generalized Newton constitutive law in two-dimensional bounded domains. The main contributions include the establishment of a pullback attractor for the solutions operator, the verification of the existence of statistical solutions through the construction of invariant Borel probability measures, and the proof that the statistical solutions possess degenerated regularity of Lusin's type under certain conditions on the Grashof number.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
J. L. Boldrini, E. Notte-Cuello, M. Poblete-Cantellano, L. Friz, M. A. Rojas-Medar
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
(2016)
Article
Mathematics, Applied
R. de Aguiar, B. Climent-Ezquerra, M. A. Rojas-Medar, M. D. Rojas-Medar
JOURNAL OF MATHEMATICAL FLUID MECHANICS
(2017)
Article
Mathematics, Applied
Pablo Braz E. Silva, FelipeW. Cruz, Marko A. Rojas-Medar
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2017)
Article
Physics, Particles & Fields
Ivan Gonzalez, Bernd A. Kniehl, Igor Kondrashuk, Eduardo A. Notte-Cuello, Ivan Parra-Ferrada, Marko A. Rojas-Medar
Article
Mathematics, Applied
V. Vivanco-Orellana, R. Osuna-Gomez, B. Hernandez-Jimenez, M. A. Rojas-Medar
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
(2018)
Article
Mathematics, Applied
Miguel Loayza, Maria D. Rojas-Medar, Marko A. Rojas-Medar
APPLICABLE ANALYSIS
(2019)
Article
Mathematics, Applied
P. Braz e Silva, F. W. Cruz, M. A. Rojas-Medar, E. G. Santos
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2019)
Article
Operations Research & Management Science
Marko Antonio Rojas-Medar, Camila Isoton, Lucelina Batista dos Santos, Violeta Vivanco-Orellana
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2020)
Article
Mathematics, Applied
E. Ortega-Torres, M. Poblete-Cantellano, M. A. Rojas-Medar
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
(2020)
Article
Mathematics
Anibal Coronel, Fernando Huancas, Esperanza Lozada, Marko Rojas-Medar
Summary: The paper investigates a control problem for an ecological model given by a reaction-diffusion system, reformulating it as an optimal control problem by introducing an appropriate cost function. The research provides a well-posedness framework of the mathematical model, studies the differentiability properties of the cost function, and proves the existence of optimal solutions, an adjoint state, and a characterization of the control function.
Article
Operations Research & Management Science
A. S. Melo, L. B. dos Santos, M. A. Rojas-Medar
Summary: This research presents higher-order necessary optimality conditions for mixed-constrained problems, introducing new generalized regularity conditions and deriving Karush-Kuhn-Tucker type results. The study also discusses the connections between these new regularity conditions and the Lagrange multipliers set, with examples provided for illustration.
Article
Computer Science, Theory & Methods
A. Baez-Sanchez, A. Flores-Franulic, A. C. Moretti, Y. Chalco-Cano, M. A. Rojas-Medar
Summary: In this article, we approximate a given fuzzy number by a unique polygonal fuzzy number using the weighted L-2 metric to preserve its main characteristics. We show that this polygonal approximation is equivalent to a finite-dimensional strict convex quadratic optimization problem with linear inequality and equality constraint. We present efficient solution methods and provide several examples for illustration. We also obtain properties of invariance of the approximation operator. The results extend and improve the methods for weighted trapezoidal approximation and piecewise linear approximation of fuzzy numbers.
FUZZY SETS AND SYSTEMS
(2022)
Article
Mathematics, Applied
Jose L. Boldrini, Rogerio de Aguiar, Marko A. Rojas-Medar, Maria D. Rojas-Medar
Summary: In this work, we investigate the optimal control problem for bioconvective flows, which are caused by differences in concentration of upward swimming microorganisms in fluid. We firstly discuss the existence of weak solutions for the mathematical fluid model, and then prove the existence of optimal controls and obtain the corresponding first-order optimality conditions using the Dubovitskii-Milyutin formalism.
ACTA APPLICANDAE MATHEMATICAE
(2022)
Article
Mathematics, Applied
Anibal Coronel, Enrique Fernandez-Cara, Marko Rojas-Medar, Alex Tello
Summary: In this article, we establish a priori estimates for a system of partial differential equations that describe the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The system involves the velocity and angular velocity of fluid particles, as well as the mass density and pressure distribution. We also employ the Helmholtz decomposition to analyze the density functions.
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
(2023)
Article
Mathematics, Applied
Anibal Coronel, Fernando Huancas, Alex Tello, Marko Rojas-Medar
Summary: In this study, new necessary conditions for the existence and uniqueness of stationary weak solutions and the existence of weak solutions for the evolution problem in the system arising from the modeling of the bioconvective flow problem are introduced. The analysis is based on the application of the Galerkin method, with a system consisting of three equations: the nonlinear Navier-Stokes equation, the incompressibility equation, and a parabolic conservation equation, where the unknowns are the fluid velocity, the hydrostatic pressure, and the concentration of microorganisms. Homogeneous zero-flux-type boundary conditions are considered for the cases of fluid velocity and microorganism concentration.
